Absolute Value Equation Game (Level 4)

Absolute Value Equation Game (Level 4)
This game combines everything you’ve learned from Level 1, Level 2, and Level 3. To solve k|x + a| = b, you must first divide both sides by k to isolate the absolute value. Once isolated, you split the equation into two cases and solve for x.
Scroll down the page for a more detailed explanation.
 
Check out these other Absolute Value Equation games:
Solve Absolute Value Equations: Level 1 (|x|=a)
Solve Absolute Value Equations: Level 2 (|x| ± a=b, a|x|=b)
Solve Absolute Value Equations: Level 3 (|x ± b|=a)
Solve Absolute Value Equations: Level 4 (k|x ± b|=a)
 

 

How to play the “Solve absolute value equation game”
When a new equation like 3|x - 2| = 12 appears, follow these steps:
Step A: Isolate the Bars
Divide the number on the right by the number in front of the bars (k).
Example: 12 ÷ 3 = 4.
Now you are solving |x - 2| = 4.
Step B: Evaluate the “No Solution”
If the result of your division is a negative number, stop immediately and click “No Solution”.
Step C: Solve the Two Cases
Take your result from Step A and create two paths:
Positive path: x - 2 = 4 → x = 6
Negative path: x - 2 = -4 → x = -2
Step D: Select & Check
Click both 6 and -2 on the grid, then hit Check Solutions.

Controls & Interface
Score Display: Tracks your accuracy.
The Grid: You can select multiple buttons. If an equation has two solutions, you must click both before hitting submit.
Color Coded Feedback:
Blue: Currently selected.
Green: The correct answer(s).
Red: A wrong choice you made.
 

How to solve absolute equations of the form k|x+a|=b
Step 1: Isolate the Absolute Value
Before you can address what is inside the bars, you must get the absolute value expression by itself. Since k is multiplying the absolute value, you use the inverse operation: division.
Divide both sides of the equation by k.
New Form: \(|x + a| = \frac{b}{k}\)

Step 2: Evaluate the Result
Look at the value on the right side (the result of \(\frac{b}{k}\)). This tells you how many solutions exist:
If negative: There is No Solution. Distance cannot be negative.
If zero: There is one solution.If positive: There are two solutions.

Step 3: Split into Two Cases
If the result is positive, you must remove the bars by “splitting” the equation into two separate linear paths. This accounts for the fact that the expression inside the bars could have been positive or negative before the absolute value was applied.
Case 1 (Positive): \(x + a = \frac{b}{k}\)
Case 2 (Negative): \(x + a = -\frac{b}{k}\)

Step 4: Solve for x
Solve both equations by isolating x. This usually involves subtracting or adding a to both sides.Example: 2|x + 3| = 10
Isolate: Divide by 2 → |x + 3| = 5
Split:
x + 3 = 5 → x = 2
x + 3 = -5 → x = -8

 

This video gives a clear, step-by-step approach to solving absolute value equations.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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